Compound interest is a very powerful way to save for your retirement. Saving a little and giving it time to grow is often more effective than saving a lot over a short period of time. To illustrate this,suppose your goal is to save $1 million by the age of 70. What amount of money will be saved by socking away $3,038 per year starting at age 23 with a 7% annual interest rate. Will you achieveyour goal using the long-term savings plan? What amount of money will be saved by socking away $20,406 per year starting at age 48 at the same interest rate? Will you achieve your goal usingthe short-term savings plan?Click the icon to view the interest and annuity table for discrete compounding when i = 7% per year.CThe future equivalent of the long-term savings plan is $ 1,000,184. (Round to the nearest dollar.)You will achieve your goal using the long-term savings plan.The future equivalent of the short-term savings plan is $. (Round to the nearest dollar.)

Answered: Compound interest is a very powerful…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Compound interest is a very powerful way to save for your retirement. Saving a little and giving it time to grow is often more effective than saving a lot over a short period of time. To illustrate this,
suppose your goal is to save $1 million by the age of 70. What amount of money will be saved by socking away $3,038 per year starting at age 23 with a 7% annual interest rate. Will you achieve
your goal using the long-term savings plan? What amount of money will be saved by socking away $20,406 per year starting at age 48 at the same interest rate? Will you achieve your goal using
the short-term savings plan?
Click the icon to view the interest and annuity table for discrete compounding when i = 7% per year.
C
The future equivalent of the long-term savings plan is $ 1,000,184. (Round to the nearest dollar.)
You will achieve your goal using the long-term savings plan.
The future equivalent of the short-term savings plan is $. (Round to the nearest dollar.)

Expert Solution

Step 1: Define the problem-mjhcc

An annuity is defined as a series of payments which are of fixed amounts at fixed intervals.

There are two types of annuities:

Ordinary Annuity- Where payment is made at the end of each period
Annuity Due- Where Annuity is made at the beginning of each period.

From the question, it is given that the goal is to save $1 Million by the age of 70.

The Future Value of an Ordinary Annuity can be calculated by using the following formula:

$F V equals C over r open square brackets left parenthesis 1 plus r right parenthesis to the power of n minus 1 close square brackets W h e r e space C space i s space f i x e d space i n s t a l l m e n t s r space i s space t h e space r a t e space o f space i n t e r e s t n space d e n o t e s space t h e space n o. space o f space i n s t a l l m e n t s$

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